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ID:52310369
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页数:9页
时间:2020-03-26
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1、ListofintegralsofrationalfunctionsThefollowingisalistofintegrals(antiderivativefunctions)ofrationalfunctions.Forothertypesoffunctions,seelistsofintegrals.MiscellaneousintegrandsAnyrationalfunctioncanbeintegratedusingpartialfractionsinintegration,bydecomposingtherationalfunctionintoasumoffunctio
2、nsoftheform:,andIntegrandsoftheformmnx(ax+b)[1]Moregenerally,(Cavalieri'squadratureformula)Integrandsoftheformm2nx/(ax+bx+c)ForIntegrandsoftheformmnpx(a+bx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0
3、.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Integrandsoftheform(mnpA+Bx)(a+bx)(c+dx)(e+fx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsm,nandptoward0.Thesereductionformula
4、scanbeusedforintegrandshavingintegerand/orfractionalexponents.SpecialcasesofthesereductionsformulascanbeusedforintegrandsoftheformbysettingBto0.Integrandsoftheformmnnpnqx(A+Bx)(a+bx)(c+dx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappli
5、edtodrivetheexponentsm,pandqtoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Specialcasesofthesereductionsformulascanbeusedforintegrandsoftheformandbysettingmand/orBto0.Integrandsoftheform(m2p2d+ex)(a+bx+cx)whenb−4ac=0Theresultingintegrandsareofthesa
6、meformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Specialcasesofthesereductionsformulascanbeusedforintegrandsoftheformwhenbysettingmto0.Integrandsofthefo
7、rm(m2pd+ex)(A+Bx)(a+bx+cx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/or
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